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Citation analysis, as a tool for quantitative studies of science, has longemphasized direct citation relations, leaving indirect or high order citationsoverlooked. However, a series of early and recent studies demonstrate theexistence of indirect and continuous citation impact across generations. Addingto the literature on high order citations, we introduce the concept of acitation cascade: the constitution of a series of subsequent citing eventsinitiated by a certain publication. We investigate this citation structure byanalyzing more than 450,000 articles and over 6 million citation relations. Weshow that citation impact exists not only within the three generationsdocumented in prior research, but also in much further generations. Still, ourexperimental results indicate that two to four generations are generallyadequate to trace a work's scientific impact. We also explore specificstructural properties such as depth, width, structural virality, and size,which account for differences among individual citation cascades. Finally, wefind evidence that it is more important for a scientific work to inspire transdomain (or indirectly related domain) works than to receive only intra domainrecognition in order to achieve high impact. Our methods and findings can serveas a new tool for scientific evaluation and the modeling of scientific history.

Citation Cascade and the Evolution of Topic Relevance